scholarly journals On a Certain Method of Selection of Domain for Finite Element Modelling of the Layered Elastic Half-Space in the Static Analysis of Flexible Pavement

2012 ◽  
Vol 58 (4) ◽  
pp. 477-501
Author(s):  
M. Nagórska
Keyword(s):  
Half Space ◽  
Mechanistic Model ◽  
Elastic Half Space ◽  
Original Method ◽  
Fe Model ◽  
Linear Elastic ◽  
Road Pavement ◽  
Viscoelastic Layers ◽  
Selection Of ◽  
Layered Half Space

AbstractIn the flexible road pavement design a mechanistic model of a multilayered half-space with linear elastic or viscoelastic layers is usually used for the pavement analysis.This paper describes a domain selection for the purpose of a FE model creating of the linear elastic layered half-space and boundary conditions on borders of that domain. This FE model should guarantee that the key components of displacements, stresses and strains obtained using ABAQUS program would be in particular identical with those ones obtained by analytical method using VEROAD program.It to achieve matching results with both methods is relatively easy for stresses and strains. However, for displacements, using FEM to obtain correct results is (understandably) highly problematic due to infinity of half-space. This paper proposes an original method of overcoming these difficulties.

Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

1989 ◽  
Vol 56 (2) ◽  
pp. 251-262 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Contact Region ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Complete Contact ◽  
The One ◽  
Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

Some Axisymmetric Problems for Layered Elastic Media: Part II—Solutions for Annular Indenters and Cracks

1989 ◽  
Vol 56 (4) ◽  
pp. 807-813 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Half Space ◽  
Contact Region ◽  
Singular Integral Equations ◽  
Integral Transforms ◽  
Lower Surface ◽  
Elastic Half Space ◽  
Solution Technique ◽  
Physical Parameters ◽  
Annular Crack ◽  
Layered Half Space

In Part I, the multiple contact region solutions for an axisymmetric indenter were presented. The solution technique utilized integral transforms and singular integral equations. The emphasis there was the study of the conditions of contact as a function of the physical parameters of the indenter and the layered elastic half space. The method and results were similar to those for the analogous plane-strain problem that was studied in Shield and Bogy (1989). However, several differences in detail were required for the analysis of the axisymmetric geometry. In this Part II, the solution of Part I is used to study some related problems that have been considered previously in the literature for homogeneous half spaces. First we solve the problem of the axisymmetric annular indenter for the layered half space. Multiple contact region solutions are studied and the problem of an axisymmetric punch with internal pressure is solved for the layered half space and also for the special case of a layer with a traction-free lower surface. Finally, the problem of an annular crack in a homogeneous or layered structure is solved.

ACOUSTIC EMISSION FROM PLASTIC SOURCES

2001 ◽  
Vol 09 (04) ◽  
pp. 1329-1345
Author(s):  
FRANZ ZIEGLER
Keyword(s):  
Acoustic Emission ◽  
Half Space ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Small Scale ◽  
Line Load ◽  
Linear Elastic ◽  
Spherical Waves ◽  
Incremental Formulation ◽  
Observation Times

Monitoring of structures which may be subjected to overloads can be based on observing signals emitted in the course of developing defects. Ductile structures react on overloads by the formation of (small scale) plastic zones. Within the linear elastic background concept such an event is considered by the formation of sources of eigenstress. Since a direct description of the source characteristics is rather cumbersome we choose the time convolution of the imposed plastic strains with the complementary Green's stress dyadic to describe the signal of the acoustice mission. Thus, the dynamic generalization of Maysel's formula of thermo-elasticity, to include all kinds of eigenstrains, enters the field of computational acoustics. In that context, the novel contribution of this paper to acoustic emission and monitoring of (layered) structures is the formulation of the full 3-D problems and the introduction of the generalized rays in the background considering an instantaneous oblique force point source at the transducer's location. That means, all the information on the wave guide is contained in the Green's stress dyadic. The expansion into plane waves of cylindrical or spherical waves propagating in a layered elastic half-space or plate proves to be quite efficient for short observation times. Even the divergence effects of dipping interfaces of wedge-type layers are perfectly included by proper coordinate rotations and the exact "seismograms" are observed at a point receiver (where the localized plastic source is assumed to develop, commonly buried and often localized at an interface) from any source located at the hypo center (the site of the transducer in receiving mode, commonly placed at the "outer" surface). This nontrivial technique relies on the invariance of the phase function (arrival time) and of the infinitesimal amplitude of the plane waves in the ray expansion. The concept of the elastic background is illustrated by elastic-viscoplastic waves propagating in thin rods and subsequently extended to the 3-D problem of spherical waves with point symmetry. In that context and in an incremental formulation, the notion of plastic sources is introduced, which emit elastic waves in the background. Finally, the full 3-D problem in a layered half space or layered plate is solved in terms of generalized rays to be received at a transducer in receiving mode. Taking into account the progress in symbolic manipulation with integrated numeric capabilities (e.g., of Mathematica), such a formulation seems timely and may prove to be competitive to the entirely computational Finite Element Method of analysis of signals received from plastic sources. Time signatures of Green's displacement components at the surface of a half-space are illustrated when produced by a vertical, horizontal and inclined line load with a triangular time source function, respectively.

Elastic Contact Between a Geometrically Anisotropic Bisinusoidal Surface and a Rigid Base

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Yang Xu ◽  
Amir Rostami ◽  
Robert L. Jackson
Keyword(s):  
Numerical Solutions ◽  
Numerical Models ◽  
Elastic Half Space ◽  
Asymptotic Solutions ◽  
Rigid Base ◽  
Fe Model ◽  
Linear Elastic ◽  
Principal Directions ◽  
Complete Contact ◽  
Elliptic Contact

In the current study, a semi-analytical model for contact between a homogeneous, isotropic, linear elastic half-space with a geometrically anisotropic (wavelengths are different in the two principal directions) bisinusoidal surface on the boundary and a rigid base is developed. Two asymptotic loads to area relations for early and almost complete contact are derived. The Hertz elliptic contact theory is applied to approximate the load to area relation in the early contact. The noncontact regions occur in the almost complete contact are treated as mode-I cracks. Since those cracks are in compression, an approximate relation between the load and noncontact area can be obtained by setting the corresponding stress intensity factor (SIF) to zero. These two asymptotic solutions are validated by two different numerical models, namely, the fast Fourier transform (FFT) model and the finite element (FE) model. A piecewise equation is fit to the numerical solutions to bridge these two asymptotic solutions.

On the Effects of Residual Stress in Microindentation Tests of Soft Tissue Structures

2004 ◽  
Vol 126 (2) ◽  
pp. 276-283 ◽  
Author(s):  
Evan A. Zamir ◽  
Larry A. Taber
Keyword(s):  
Residual Stress ◽  
Soft Tissue ◽  
Elastic Foundation ◽  
Elastic Properties ◽  
Material Properties ◽  
Soft Tissues ◽  
Elastic Half Space ◽  
Fe Model ◽  
Linear Elastic ◽  
Tissue Structures

Microindentation methods are commonly used to determine material properties of soft tissues at the cell or even sub-cellular level. In determining properties from force-displacement (FD) data, it is often assumed that the tissue is initially a stress-free, homogeneous, linear elastic half-space. Residual stress, however, can strongly influence such results. In this paper, we present a new microindentation method for determining both elastic properties and residual stress in soft tissues that, to a first approximation, can be regarded as a pre-stressed layer embedded in or adhered to an underlying relatively soft, elastic foundation. The effects of residual stress are shown using two linear elastic models that approximate specific biological structures. The first model is an axially loaded beam on a relatively soft, elastic foundation (i.e., stress-fiber embedded in cytoplasm), while the second is a radially loaded plate on a foundation (e.g., cell membrane or epithelium). To illustrate our method, we use a nonlinear finite element (FE) model and experimental FD and surface contour data to find elastic properties and residual stress in the early embryonic chick heart, which, in the region near the indenter tip, is approximated as an isotropic circular plate under tension on a foundation. It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation. This method may not be as useful, however, for structures that behave as a beam on a foundation.

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